Prime Submodules of Graded Modules

Let G be a group, R be a G-graded ring and M be a G-graded R-module. Suppose P is a prime ideal of Re and g G G. In this article, we define Mg (P) = {m G Mg : Am C PMg for some ideal A of Re satisfying A C P}that is an Re-submodule of Mg, and we investigate some results on this submodule. Also, we i...

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Autores principales:	Abu-Dawwas,Rashid, Al-Zoubi,Khaldoun, Bataineh,Malik
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2012
Materias:	Graded rings graded modules prime submodules
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000400004
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spelling	oai:scielo:S0716-091720120004000042012-12-18Prime Submodules of Graded ModulesAbu-Dawwas,RashidAl-Zoubi,KhaldounBataineh,Malik Graded rings graded modules prime submodules Let G be a group, R be a G-graded ring and M be a G-graded R-module. Suppose P is a prime ideal of Re and g G G. In this article, we define Mg (P) = {m G Mg : Am C PMg for some ideal A of Re satisfying A C P}that is an Re-submodule of Mg, and we investigate some results on this submodule. Also, we introduce a situation where if N is a gr-prime R-submodule of M ,then (Ng : Mg) is a maximal ideal of Re. We close this article by introducing a situation where if N is a gr- R-submodule ofM such that Ne is a weakly prime Re-submodule of Me, then Ng is a prime Re-submodule of Mg.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.31 n.4 20122012-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000400004en10.4067/S0716-09172012000400004
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Graded rings graded modules prime submodules
spellingShingle	Graded rings graded modules prime submodules Abu-Dawwas,Rashid Al-Zoubi,Khaldoun Bataineh,Malik Prime Submodules of Graded Modules
description	Let G be a group, R be a G-graded ring and M be a G-graded R-module. Suppose P is a prime ideal of Re and g G G. In this article, we define Mg (P) = {m G Mg : Am C PMg for some ideal A of Re satisfying A C P}that is an Re-submodule of Mg, and we investigate some results on this submodule. Also, we introduce a situation where if N is a gr-prime R-submodule of M ,then (Ng : Mg) is a maximal ideal of Re. We close this article by introducing a situation where if N is a gr- R-submodule ofM such that Ne is a weakly prime Re-submodule of Me, then Ng is a prime Re-submodule of Mg.
author	Abu-Dawwas,Rashid Al-Zoubi,Khaldoun Bataineh,Malik
author_facet	Abu-Dawwas,Rashid Al-Zoubi,Khaldoun Bataineh,Malik
author_sort	Abu-Dawwas,Rashid
title	Prime Submodules of Graded Modules
title_short	Prime Submodules of Graded Modules
title_full	Prime Submodules of Graded Modules
title_fullStr	Prime Submodules of Graded Modules
title_full_unstemmed	Prime Submodules of Graded Modules
title_sort	prime submodules of graded modules
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2012
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000400004
work_keys_str_mv	AT abudawwasrashid primesubmodulesofgradedmodules AT alzoubikhaldoun primesubmodulesofgradedmodules AT batainehmalik primesubmodulesofgradedmodules
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Prime Submodules of Graded Modules

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